Solid State - Result Question 44
####44. Chromium metal crystallises with a body centred cubic lattice. The length of the unit edge is found to be $287 pm$. Calculate the atomic radius. What would be the density of chromium in $g / cm^{3}$ ?
(1997, 3M)
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Solution:
- In bcc unit cell, $4 r=\sqrt{3} a$
$\Rightarrow \quad r(Cr)=\frac{\sqrt{3} a}{4}=\frac{\sqrt{3}}{4} \times 287 pm=124.3 pm$
Density of solid $=\frac{N M}{N _A \cdot a^{3}}$
$N=$ Number of atoms per unit cell, $\quad M=$ Molar mass
$a^{3}=$ Volume of cubic unit cell, $\quad N _A=$ Avogadro’s number
$$ =\frac{2 \times 52 g}{6.023 \times 10^{23}} \times\left(\frac{1}{2.87 \times 10^{-8} cm}\right)^{3}=7.3 g / cm^{3} $$
